On blocking sets of quadrics
type: Item
instance of: scholarly article
title: On blocking sets of quadrics
zbMATH Open document ID: 0970.51010
DOI: 10.1007/BF01220310
author: Klaus Metsch
published in: Journal of Geometry
publication date: 2001-10-16T00:00:00Z
review text: A blocking set \(B\) of a quadric \(Q\) with respect to \(s\)-dimensional subspaces is a set of points of \(Q\) such that every \(s\)-dimensional subspace contained in the quadric \(Q\) meets \(B\) in at least one point. A blocking set with respect to lines is simply called blocking set. In the paper under review the three smallest blocking sets with respect to lines of the parabolic quadric \(Q(2n,q)\) \((n\geq 3)\) and the two smallest blocking sets with respect to lines of the hyperbolic quadric \(Q^+(2n+1,q)\) \((n\geq 2)\) are determinated. These blocking sets are obtained intersecting the quadric with a hyperplane; if such a hyperplane is tangent to the quadric, then the intersection is not a minimal blocking set, the pole of \(H\) has to be removed to obtain a minimal blocking set. This result is obtained as a consequence of two theorems regarding blocking sets of upper bounded size in \(Q^+(2n+1,q)\) and \(Q(2n,q)\), respectively.
reviewed by: Guglielmo Lunardon
Mathematics Subject Classification ID: 51E20
zbMATH DE Number: 1443435
zbMATH Keywords: blocking sets
zbMATH Keywords: quadric
MaRDI profile type: Publication
cites work: Some \(p\)-ranks related to orthogonal spaces
cites work: Baer subplanes and blocking sets
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cites work: Q4370894
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full work available at URL: https://doi.org/10.1007/bf01220310
OpenAlex ID: W2044705423
description: scientific article; zbMATH DE number 1443435